guberman_the development of everyday mathematics in brazilian children

8/2/2019 Guberman_The Development of Everyday Mathematics in Brazilian Children

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G|BLRI@H* S^LULH L ( ^ml Nluljavilh ~ ae Lulr{n`{ I`~mli `~kcs khBr`tkjk`h Cmkjnrlh wk~mJkik~ln Eari` j Ln|c`~kah( C M K J N N L Z ' L J A V I L S ^ * 0;;5*57 *056;)0523 ( ^ ml sackac|j~|r`j cah~l}~kh wmkcm cmkjnrlh `cp|krl `hn |sl lulr{n`{ i`~mli`~kcs w`s s~|nkln khBr`tkjk`h sm`h~{~awhcaii|hk~kls( Gmkjnrlh's nluljavkhg i`~mli`~kc`j `bkjk~kls `hn |sl ae c|rrlhc{ kh sajukhg cai)ilrck`j vrabjlis wlrl khuls~kg`~ln( Kh~lruklws wk~m ~ml v`rlh~s ae 06< cmkjnrlh erai > ~a 0>{l`rs ae `gl khnkc`~ln ~m`~* wmlh slh~ ~a iòl v|rcm`sls `~ jac`j s~`hns* ~ml vrabjlis lh~`kjlni ~ml rlsva hskbkjk~kls v`rlh~s `sskghln ~a cmkjnrlh khuajuln grl`~lr `rk~mil~kc`j caivjl}k~{ wk~mkhcrl`skhg `gl( Gmkjnrlh's `cc|r`c{ `hn s~r`~lg{ |sl ah `rk~mil~kc ~`sos skikj`r ~a ~ml vrabjlislhca|h~lrln khcaiilrck`j ~r`hs`c~kahs rlul`jln4 -` + i`h{ cmkjnrlh |sln c|rrlhc{ ~a `kn ~mlkrvramjli sajukhg*) -b + wk~m khcrl`skhg `gl* c|rrlhc{ |sl nlcjkhln? `hn -c+ cmkjnrlh's c|rrlhc{ |slvragrlssln erai gjab`j ls~ki`~ls ~a ~ml ilh~`j nlcaivask~kah `hn i`hkv|j`~kah ae c|rrlhc{)u`j|ls( ^ ml i`~mli`~kc`j caivjl}k~{ ae cmkjnrlh's caiilrck`j ~r`hs`c~kahs carrlj`~ln skghkek)c`h~j{ wk~m ~mlkr i`~mli`~kcs vlreari`hcl lulh wmlh `gl* gr`nl i scmaaj* `hn {l`rs ae scmaaj)khg wlrl s~`~ks~kc`jj{ cah~rajjln ^ ml rls|j~s vrauknl luknlhcl ~m`~ b{ `nd|s~khg ~ml i `~mli`~kc`jcaivjl}k~{ ae cmkjnrlh's caiilrck`j ~r`hs`c~kahs* v`rlh~s e`ckjk~`~l cahhlc~kahs bl~wllh cmkj)nrlh's nluljavkhg caivl~lhcl `hn ~mlkr lulr{n`{ `c~kuk~kls(

J l ` r h k h g `hn sajukhg vrabjlis kh -Gkhsb|rg* Vashlr* % R|ssljj* 0;=0? I`skh)scmaaj ae~lh nkeelr erai jl`rh khg `hn sajukhg gkj`* 0;; 3? H| hls l ~ ` j ( * 0;;03? S `}l* 0;; 0?vrabjlis a|~sknl ae scmaaj( Kh scmaaj* cmkj) S crkbhlr* 0;=5+( C ai ilrck`j ~r`hs`c~kahsnrlh ~{vkc`jj{ waro `jahl* wk~ma|~ ~aajs* `hn mùl bll h mkgm jkgm~ln `s `h lsvlck`jj{ rkcm`rl l}vlc~ln ~a `cp| krl `hn `vvj{ glhlr`j nai`kh ear `cp|krkhg i`~mli`~kc`j ohawj)r|jls ~a vrabjli s ae~lh rli auln erai `h{ lngl `hn sokjj4 C mkjnrlh `hn `n|j~s wma lh)il`hkhge|j cah~l}~( Kh cah~r`s~* jl`r hkh g g`gl rlg|j`rj{ khcaiilrck`j l}cm`hgl nks)`hn rl`sahkhg a|~sknl ae scmaaj `rl ae~lh vj`{ iarl `nu`hcln i`~mli `~kcs ~m`h nag|knln b{ a~mlrs* liblnnln khil`hkhge|j vlav jl wk~m jlss khuajuli lh~ kh caiilrcl`c~kuk~kls* `hn |sl ohawjlngl jkholn ~a~ml -V ashlr* 0;=2? S `d4l* 0;=2* 0;;0+(vrabjli sk~|`~kah* s|cm `s ~ml abdlc~s blkhgcahsknlrln* ~ml v`r~kckv`h~s 'ga`js * `hn ~ml (jkX| k k k kù`kj`bjl c|j~|r`j `r~ke`c~s -G` rnhlr* 0;;0 ? @j~ma|g m ~ml lulr{n`{ i`~mli`~kcsG|blri`h % Grllhekljn* 0;;0? H |hl s * e l na|~sknl ae scmaaju`rka|sj{ c`jjln kh)Scmjkli`hh( % C `rr`mlr* 0;;3? Rlshkco $XX' ~"k~kul* ar`j ar s~rll~ i`~mli`~)0;=5* 0;=7+( XXXX$ cm`r`c~lrktln b{ k~s ejl}kbkjk~{-Scrkbhlr* 0;=5+* lulr{n`{ i`~mli`~kcs m`sVlrm`vs ~ml nai`kh khwm kcm lulr{n `{ caiiah cm`r`c~lrks~kcs `crass cah~l}~s aerl`sahkhg m`s bllh s~|nkln ias~ ~mara|gmj{ |sl( C `rr`mlr* C `rr`mlr* `hn Scmjkli`hhks i`~mli `~kcs( Rlsl`rcmlrs mùl rlva r~ln -0;=7+ vrauknl h l}ìvjl ~m`~ mkgmjkgm~sjkhos bl~w llh ~m l i`~mli`~kcs ae ba~m cmkj) ~ml h`~|rl ae lulr8'n`{ i`~mli `~kcs `hn mawnrlh `hn`n|j~s `hn ~jklkr v`r~kckv`~kah kh k~ nkeelrs erai ~ml i`~mli`~kcs ~{vkc`jj{u`rka|s `c~kuk~kls4 sljjkhg c`hn{* c4krvlh~lr) ~`|gm ~ `h n |sl n khscmaaj( Kh ~mks khs~`hcl*khg* ekjjkhg arnlrs kh `n`kr8'* khs ~`jjkh g ejaars ` Br`tkjk`h ~mkrn gr`nlr ~rkls ~a sajul ~ml

V`r~k`j s|vvar~ ear ~mks vradlc~ w`s vrauknln b{ ~ml H`~kah`j Scklhcl Ea|hn`~kah -BHS=


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0 5 0 6 C m k j n N l { l j a v i l h ~vrabjli 266 3< |skhg wrk~~lh* scmaaj)jkolvracln|rls -v( ;


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S ~lulh R( G|b lri`h 05 00`cmklulilh~s* `gl* `hn lulr{n`{ `c~kuk~klskhnlvlhnlh~ ae scmaaj l}vlrklhcl(

^ mra|gm a bslru`~kahs `hn vrljkikh`r{)kh~lruklws* ahl i`~mli`~kc`j `c~kuk~{lilrgln `s ` eac|s ear s~|n{4 Hl`rj{ `jj cmkj)nrlh wlrl slh~ b{ ~mlkr v`rlh~s* ae~4lh slu)lr`j ~kils ` n`{* ~a iòl si`jj v|rcm`sls-l(g(* san`* brl`n + `~ jac`j s~`h ns( C mkjn rlherai ` wknl r`hgl ae `gls v`r~kckv`~ln kh~mlsl ~r`hs`c~kahs* `hn ~ml vrabjlis ~m`~lilrgln kh ~mli `vvl`rln ~a lh~`kj cmkj)nrlh's ias~ caivjl} i`~mli`~kcs |s`gl(^ml Nluljavilh~ ae Cmkjnrlh's Lulr{n`{I`~mli`~kcs `hn C|rrlhc{ \sl^ a g`kh khskgm~ kh~a ~ml n luljavi lh~ aelulr{n`{ i`~mlk|`~kc`j rl`sahkhg* cmkjnrlherai 5 ~a 0> {l`rs ae `gl wlrl `soldn ~a sajul`rk~mil~kc vrabjlis skikj`r ~a ~ml ahls ~m`~lilrgln kh ~mlkr caiilrck`j ~r`hs`c~kahs(Ba~m `cc|r`c{ `hn vrabjli)sajukhg s~r`~l)gkls wlrl l}ìkhln(

C mkjnrl h's `bkjk~{ ~a |sl ia hl{ kh saju)khg vrabjlis w`s `sslssln b{ vrlslh~khg~`sos ba~m wk(~m `hn wk~ma| ~ ia hl{( ^ a jaaoiarl cjaslj{ `~ ~ml nl ulja vi lh~ ae `rk~mil~)kc`j nlcarhvask~kah sokjjs* ~ml eari ae c|r)rlhc{ w`s u`rkln( Ear sail vrabjlis* cmkj)nrlh Wlrl gkulh c|rrlhc{ ~m`~ ca|jn blv`r~k~kahln kh~a gra|vs rlvrlslh~khg ~ml cas~ae làjs ~a)~8l)v|rcm`sln k~li( Gra|vkhg c|r)rlhc{ kh~a ~ml ìa|h~ hllnln ear l`cm k~li*wmkcm cmkjcjrlh |sln ae~lh kh vkja~ waro* rl)p|krls knlh~ke{khg `hn `nnkhg |hk~s ae c|r)rlhc{ b|~ nals ha~ hlclss`rkj{ jl`n cmkjnrlh~a nlcaivasl c|r~lhc{ u`j|ls( C ahsl)p|lh~j{* lmkjnrlh wlrl `soln `jsa ~a sajulvrabjlis wkkm( c|rrlhc{ ~m`~ ca|jn ha~ blgra|vln kh~a ~ml vrkcl ae l`cm k~li* s|cm `sb|{ khg k~lis cas~khg C r.0 `hn 0> {l`rs ae `gl `hn ~mlkr v`r)lh~s( ^ ml cmkjnrlh `hn v`rlh~s wlrl rl)cr|k~ln b{ Br`tkjk`h |hkulrsk~{ s~|nlh~s khsm`h~{~awh caii|hk~kls kh `hn `ra|hn Rl)ckel( ^ ml cmkjnrlh wl rl v`r~k~kahln kh~a ea|r`gl gra|vs4 ~ml il`h `gl* gr`nl jlulj* `hn{l`rs ae scmaaj `~jlhn`hcl ear l`cm gra|v `rlvrlslh~ln kh ^ `bjl 0( ^ mlrl w lrl `vvra}k)i`~lj{ lp|`j h|iblrs ae ba{s `hn gkrjs khl`cm gra|v(Vracln|rlsV`rlh~s wlrl kh~lruklwln `~ mail cah)clrhkhg ~mlkr cmkjnrlh's caiilrck`j ~r`hs`c)

') @~ ~ml ~ki l ae n`~` cajjlc~kah* ~ml Br`tkjk`h |hk~ ae c|rrlhc{ w`s ~ml cr|tlkra -C r.+( ^ mlias~ caiiah |hk~s ae c|rrlhc{ w lrl khcj|nln kh ~ml s~|n{? C rS


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0502 C mkjn N luljavilh~^ @ B J L 0

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> ) < 5 ) = ; ) 0 0 0 2 ) 0>H| ib lr ae lmkjnrlh 06 3; 2; 27@gl -{l`rs+ >(= 7(5 06(< 03(3-(5+ -(;+ -(=+ -(;+G r`n l kh scmaa j 6(6 6(5 0(; 3(6-(6+ - < + -(=+ -0(5+[l`rs ae scmaaj `~~l hn `h cl' 6(6 0 7 3(>


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S~lulh R( G|blri`h 0503C|rrlhc{ Knlh~kekc`~kah ScrllhkhgEajjawkhg ~ml C aiilrck`j ^ r`hs`c~kahsKh~lruklw* cmkjnrlh wlrl `soln ~a knlh~ke{*kh r`hnai arnlr* ~ml sk} c|rrlhc{ nlhaikh`)~kahs |sln kh ~ml `rk~mi l~kc ~`sos( C mkjnrlhwma carrlc~j{ knlh~kekln jj sk} nlhaikh`)~kahs wlrl khuk~ln ~a v`r~kckv`~l kh ~ml `rk~m)il~kc ~`sos `sslssilh~(@rk~mil~kc ^`sosKh arnlr ~a l}ìkhl `gl)rlj`~ln smke~s khcmkjnrlh's lulr{n`{ i`~mli`~kcs* l`cm cmkjnw`s `soln ~a sajul ~ml 25 `rk~mil~kc vrab)jlis vrlslh~ln kh^ `bjl 2( Ear l`cm vrab)jli* ~ml kh~lruklwlr nlscrkbln ` ~{vkc`jcairk`lrck`j ~r`hs`c~kah( ^ml k~lis ilh)~kahln! kh ~ml v rabjli wlrl vj`cln ah ` ~`bjlkh erah~ ae ~ml cmkjn* `jahg wk~m c`rns smaw)khg ~ml h|ilrkc`j u`j|ls kh~ ml vr abj l i * `v`n ae v`vlr* `hn ` vl hc k j( C mk j nr l h w l r lkhs~r|c~ln ~a sajul ~ml vrabjlrhs mawlulr~ml{ cmasl `hn ~a l}vj`kh ~mlkr saj|~kahs `s~ml{ vracllnln( @e~lr caivjl~khg ` vrab)jli* cmkjnrlh wlrl `soln ~a cj`rkedd1 ~mlkr sa)j|~kah vraclss ke hllnln(

Cas~ `hn cm`hgl vrabjlis(â `sslss~ml `bkjk~d ' ~a |sl c|rrlhc{ ~a sajul `rk~mil)~kc vrabjlis* cmkjnrlh wlrl vrlslh~ln ekulvrabjlis ~wkcl4 ahcl wk~m c|rrlhc{ `hn

ahcl wk~ma|~ c|rrlhc{( Ear ~ml c|rrlhc{vrabjlis* cmkjnrlh wlrl gkulh ` "i ahl {ba}" v`r~k~kahln kh~a sk} slc~kahs? l`cm slc)~kah cah~`khln slulr`j |h k~s ae` c|rrlhc{ n l)haikh`~kah( C mkjnrlh w lrl `soln ~a ba~ms~`~l ~mlkr `hswlr ~a ~ml vrabjli `hn ~a gkul~ml kh~lruklwlr ~ml `vvravrk`~l ìa|h~ aeiahl{* `j~ma|gm sail cmkjnrlh nkn ha~ |sl~ml c|rrlhc{( Oa c|rrlhc{ w`s vrauknln ear~ml a~mlr cahnk~kah? ear ~mlsl ha c|rrlhc{vrabjlis* cmkjnrlh wlrl `soln ~a s~`~l ~ml`hswlr(^ ml c|rrlhc{ `hn ha c|rrlhc{ vrabjlisl~s cahsks~ln ae ~ml sìl h|ilrkc`j u`j|ls`hn `rk~mil~kc`j avlr`~kahs* b|~ ~ml ~a)bl)v|rcm`sln k~lis nlscrkbln kh ~ml vrabjlisnkeelrln( Ear ~mrll vrabjlis kh l`cm sl~*cmkjnrlh wlrl `soln ~a nl~lrikhl ~ml ~a~`jcas~ ae ` v|rcm`sl cahsks~khg ae slulr`jk~lis( Ear ~ml akjklr ~wa vrabjlis kh l`cmsl~* cmkjnrlh wlrl `soln ~a ekg|rl a|~ ~mlcm`hgl ~ml{ sma|jn rlclkul kh svlckekln~r`hs`c~kah( Ear l`cm vrabjli* cmkjnrlh rl)clkuln ahl vakh~ ear s~`~khg ~ml carrlc~ `h)swlr? vasskbjl scarls r`hgln erai 6 ~a < earl`cm cahnk~kah(I|j~kvjl k~li vrabjlis( K h ar nl r ~ag`kh iarl nl~`kjln kheaik`~kah `ba|~ cmkj)

^@BJL 2V L A B J L I S \ S L N ^ A @S S LS S C M K J N R LH 'S I @^ M LI @^ K C @ J C A I V L^ L HC L

C as~ `hn cm`hgl vrabjlis4L`cm vrabjli w`s vrlslh~ln ~wkcl* ahcl wk~m ` "iahl{ ba}" ù`kj`bjl ear ~bl cbkjnrlh ~a |sl `hnahcl wk~ma|~ iahl{(C as~ }N rabjlis40( W b`~ ks ~bl ~a~`j cas~ ke {a| w `h~ ~a b|{ ~brl l _k~li ` Y `hn l`cb cas~s C rS 266 `hn l`cb |~li cY cas~s C r.36613 W b`~ ks ~bl ~a~`j cas~ ke {a| w `h~ ~a b|{ ~wa _k~li nY * ahl _k~li lY * `hn ahl _k~li ! Y * ke l`cb_k~li nY cas~s C r.j*566 * l`cb _k~li lY cas~s C rS=66* `hn l`cb _k ~ li Y cas~s C r.( M aw i| cb cb`hgl sba|jn {a| rlllkul ke {a| b|{ _k~li gY ear C rS


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050> CmkkI Bluljavilh~kdrlh's |sl ae c|rrlhc{ kh svjuk`g caii lrck`j~r`hs`c~kah vrabjlislsvlck`jj{ ~mlkr `bkj)k~{ ~a ilh~`jj{ nlcaivasl Mkihlrkc`j u`j)|lsl`lm cmkjn w`s `soln ~a sajul 05 vrab)jlis ~m`~ u`rkln kh ~ml eari ae c|rrlhc{vrauknln( Vrabjlis cahclrhln lk~mlr ~mlh|iblr ae k~lis ~m`~ ca|jn bl ba~kgm~ wk~m` svlckekln ìa|Nk~ aE rh`hl{ ar ~ml ìa|h~-?X iahl{ hllnln ~a b|{ ` svllkekln h|iblrae k~lrhs(

Ear lkgm~ vrabjlis* cmkjnrlh wlrl vra)uknln wk~m |hk~ c|rrlhc{ch|rlhc{ ~ml{ca|jn v`r~k~kah kh~a gra|vs ~a rlvrlslh~ ~mlcas~ ae l`cm ~a)bl)v| rcm`sln k~li* ` s~r`~lg{~m`~ nals ha~ rlp|krl nlcaivaskhg h|ilrk)c`j p|`h~k~kls( Ear ~ml a~mlr lkgm~ vrabjlis*cmkjnrlh wlrl vrauknln wk~m rkah|h~~ c|r)rlhc{)chkrlhc{ ~ml{ ca|jn ha~ v`r~k~kahkh~a gra|vs ear l`cm ~a)bl)vkkrcm`sln k~li(K~ w`s l}vlc~ln ~m`~ ~ml hah|hk~ c|rrlhc{vrabjlis wa|jn lhg`gl iarl lmkjnrlh khilh~`j nlcaivask~kah s~r`~lgkls(

sl~s ae |hk ~ `hnhah|hk ~ vrabjliswlrl ' i`~cmln ear nkDekl|j~{4 @crass sl~s*vrabjlis lh~`kjln ~ml sìl h|iblr ae ~a )bl)v|rcm`sln k~lis `hn ~ml sìl ~a~`j cas~(Cmkjnrlh rlclkuln ah l vakh ~ ear l`cm carrlc~`hswlr? vasskbjl scarls r`hgln erai 6 ~a =ear l`cm vrabjli sl~(

S~^n~lg{ cankhg(^ml il~mans cmkj)nrlh |sl n ~a sajul lkgm ~ ae ~ml i |j~kvjl k~livrnbkjlis wlrl l}ìkhln(X Vrluka|s `h`j{)sls ae cmkjnrlh's kheari`j i`~mli`~kcs mùlnks~khg|ksmln bl~wllh i`hkv|j`~khg wrk~)~lh s{ibajs `hn i`hkv|j`~khg il`hkhge|jp|`h~k~kls -H|hls l~ `j( * 0;;3? Rlln % Jùl*0;7;+( Kh arnlr ~a eac|s ahcmkjnrlh's |sl aec|rrlkjc{ `hn nlcaivask~kah* ~ml vrlslh~`h`j{sks nks~khg|ksmln bl~w llh ~wa ~{vls aep|`h~k~{' i`hkv|j`~kah4 i`hkv|j`~khg c|r)rlhc{ U`j|ls `hn i`hkv|j`~khg hahc|rrlhc{u`j|ls( Cahslp|lh~j{* cmkjnrlh's saj|~kahs~a l`cm vra b jlhk w lrl c`~lgarktln `sahl ae~mrll s~e`klg~! ~{vls( Wrk~~lh c`jc|j`~kahs~r`~lgkls kh~cj|nln `jj saj|~kah `~~liv~s khwmkcm cmkjnrlh wra~l h|i blrs ah v`vlr bl)earl s~`~khg `h `hswlr -wml~mlr ar ha~ a~mlrs~r`~lgkls w lrl `jsa |sln+( Saj|~kah `~~li v~skh wmkcm cmkjnrlh nkn ha~ |sl v`vlr `hnvlh ckk wlrl cj`sskekln `s hahc|rrlhc{ s~r`~l)gkls ke cmkjnrl h s~`~ln `h `hsw lr wk~ma |~ |s)khg c|rrlhc{ `hn wk~ma|~ rlelrrkhg ~a iahl)

~`r{ u`j|ls* ar `s c|rrlhc{ s~r`~lgkls kecjkkjnkrlrk vm{skc`jj{ i`hkv|j`~ln ~ml c|r)rlac{ blearl s~`~khg `h `hswlr* ar rlelrrln~a iahl~`r{ u`j|ls n|rkhg ~mlkr saj|~kahs arwmkjl l}vj`jkkkhg maw ~ml{ `rrkuln `~ `h`hswlr(Kh arnlr ~a `h`j{tl cmkjnrlh's c|rrlhc{s~r`~lgkls kh iarl nl~`kj* ` ekul)jlulj scmlilw`s cahs~r|c~ln( Kh ~ml scmlil* vrlslh~lnkh ^`bjl 3 -`hn nlscrkbln kh iarl nl~`kj kh~ml R ls|j~s slc~kah+* mkgm lr)h| ib lrln s~r`~)lgkls lh~`kj grl`kBr nkeelrlh~k`~kaB ae c|r)rlhc { u`j|ls `hn kh crl`skh g ejl}kbkjk~{ kh i`)hkv|j`~khg ~masl u`j|ls(Rljk`bkjk~{(^ml `|~mar `hn ` rlsl`rcm`ssks~lrk~ |sln ha~ls ~òlh n|rkh g ~ml `sslss)ilh~ ~a khnlvlhnlh~j{ canl ~ml s~r`~lgkls|sln b{2> r`hnaij{ sljlc~ln s|bdlc~s nks)~rkb|~ln `lrass `glgra|vs -2;, ae `j j s|b)dlc~sy( Canlrs `grlln ah s~r`~lg{ ~{vl ear 0=3ae ~ml 0;6 vrabjli s khwmkcm ` s~r`~lg{ w`s|svn -Gpmlh's o`vv` 99X (;3+( Ae ~ml => saj|)~kahs canln b{ ba~m r`~lrs `s c|rrlhc{ i`)hkv|j`~kah* `grllkrklh~ ah s~r`~lg{ jlulj w`s

`lmkluln ear 7> ae ~mli -Camlh's o`vv` 9(=


7/15

S~lulh R( G|blri`h 050

0( L}`c~ v|rcb`sl 06 20 7 >2( Lj}vlc~ cb`hgl ;6 >> 2= >3( Cahekri cb`hgl 6 25 2> 25>( C`jc|j`~l `|rcb`sl 6 06 >0 57H '(((((( 06 3; 2; 27

nrlh `sskghln ~a l`cm `c~kuk~d' jlulj ks vrl)slh~ln kh ^`bjl +(

@ Or|so`j)W`jjks ahl)w`{ @HAU@ ahcmkjnrlh's `c~kuk~{' jluljs cahekriln ~m`~ajnlr cmkjnrlh wlrl khuajuln kh `c~kuk~kls aegrl`~lr `rk~mil~kc`j caivjl}k~{ ~m`h wlrl{a|hglr cmkjnrlh* }XA* H 9 06(;*v : (6660( Caiv`rksahs ae `nd`clh~ `glgra|vs rlul`jln ~m`~* `ccarnkhg ~a v`rlh~`jrlvar~s* 02)0>){l`r)ajns w lrl lhg`g ln kh `r)k~mil~kc`jj{ iarl caivjl} `c~kuk~kls ~m`hwlrl ;)00){l`r)ajns -I`hh)Wmk~hl{ \ 9257(


9/15

S~lulh R( G|blri`h 0507sajuln carrlcn{ iarl vrabjlis wk~m c|r)rlhc{ ~m`h wk~ma|~ c|rrlhc{* `hn ~ml 020>){l`r)ajns sajuln carrlc~j{ iarl vrabjlis~m`h nkn~ml ;)02){l`r)ajn s* wm a sajuln car)rlc~j{ iarl vrab jlis ~m`h nkn ~ml 5)=){l`r)ajns -N|hc`h v`krwksl caiv`rksahs* vs :(60+( -âg|`rn `g`khs~ ~ml khej`~kah ae `jvm`jluljs* vas~ mac v`krwksl caiv`rksahs wlrl~ls~ln |skhg `h `jvm` jlulj ae (6< nkuknln b{~ml h|i blr ae caiv`rksahs _sllM`{s* 0;=0*v ( >3){l`r)ajns( Kh cah~r`s~* ha cmkjn lulr gùl ~ml kh)carrlc~ ìa|h~ ae iahkl{ `hn s~`~ln ~mlcarrlc~ `hswlr( ^m|s* ah ` s|bs~`h~k`j h|i)blr ae vrabjlis* cmkjnrlh* lsvlck`jj{{a|hglr cmkjnrlh* wlrl c`v`bjl ae ~lhnlrkh g~ml garrlc~ ìa|h~ ae iahl{ wk~ma|~ blkhg`bjl ~a nl~lrikhl ~ml ~a~`j ìa|h~ ~ml{weddrl gkukh g( @s nksc |ssl n blja w* kh ~ ml i| j)~kvjl k ~li vrabjlis* i`h{ cmkjnrlh |slns~r`~lgkls ~m`~ skivjkekln ~ml i`~mli`~kcs aecaiilrck`j ~r`hs`c~kahs* s|cm `s nld~lrikh)

khg v`r~k`j c`jc|j`~kahs `hn v`{ilh~s*~mlrlb{ ùaknkhg ~ml hlln ~a ca|h~ a|~ ~ml~a~`j ìa|h~ ae iahl{ hllnln ear ~ml v|r)cm`sl(Kh s|ii`r{* i`h{ cmkjnrlh `~~liv~ln~a |sl c|rrlhc{ kh ~kklkr vrab jli sajukhg `hn*ear ~masl wma v`ssln ~ml c|rrlhc{ scrllh)khg* cmkjnrlh |sln c|rrlhc{ wk~m khcrl`skhgvraekcklhc{ erai 5 ~a 0> {l`rs ae `gl( Jlsserlp|lh~ |sl ae c|rrlhc{ b{ ~ml ajnlr cmkj)nrlh s|ggls~s ~ml{ m`n ù`kj`bjl ` grl`~lrrlvlr~akrl ae vrabjli)sajukhg s~r`~lgkls ~m `hnkn ~ml {a|hglr cmkjnrlh(

I|j~kvjl K~li Vrabjlis@cc|r`c{(Caiv`rkhg vlreari`hclsah ~ml |hk ~ `hn hah|hk~ c|rrlhc{ vrabjlisvrauknls iarl nl~`kjln kheari`~kah `ba|~cmkjnrlh's nluljavkhg c|rrlhc{ |sl* lsvl)ck`jj{ ~mlkr `bkjk~{ ~a nlcaivasl h|ilrkc`ju`j|ls( Wmlrl`s ah |hk~ c|rrlhc{ vrabjliscmkjnrlh ca|jn v`r~k~kah c|rrlhc{ kh~aìa|h~s lp|`j ~a ~ml cas~ ae l`cm ~a)bl)v|rcm`sln k~li* a~mlr s~r`~lgkls* s|cm `silh~`j nlcaivask~kah `hn rlgra|vkhg* wlrlhllnln ear ~ml hah|hk~ c|rrlhc{ vrabjlis(^`bjl 7 cah~`khs cmkjnrlh'sX `cc|r`c{scarls ear |hk ~ `hn hah|hk~ c|rrlhc{ vrab)jlis( @ 3 -`gl gra|v+ } 2 -cahnk~kah4|hk~ c|rrlhc{* hah|hk~ c|rrlhc{? rlvl`~ln+@HAU@ ah ~ml h|i bl r ae vrabjlis sajulncarrlc~j{ {kljnln i`kh leelc~s ae `gl gra|v*E-2* 7;+ 9 20(=* v : (660* cahnk~kah* E-j* 7;+9 07(=* v : (660* `hn `h `gl } cahnk~kahkh~lr`c~kah* E-2* 7;+ 9 7(;* v : (60( ^ml kh)~lr`c~kah smaws ~m`~ ~ml leelc~ ae c|rrlhc{u`rkln wk~m `gl gra|v? ^ml `cc|r`c{ ae ~ml

5=){l`r)ajns `hn ~ml 02)0>){l`r)ajns u r)kln ahj{ sjkgm~j{ `crass c|rrlhc{ cahnk~kahsKvs 8 (06+? kh cah~r`s~* ~ml `cc|r`c{ ae ~ml;)X00){l`r)ajns w`s skghkekc`h~j{ mkgmlr kh~ml |hk~ c|rrlhc{ cahnk~kah ~m`h kh ~ml hah)|hk~ c|rrlhc{ cahnk~kah* ~-2;+ 9


10/15

050 = Cmkjn Nluljavilh~@j~ma|gm ~ml vlreari`hcls ae ~ml 5=){l`r)ajns `hn ~ml k2))0>){l`r)(ajns wlrl |h)èelc~ln b{ ~ml eari ae c|rrlhc{* ~mlkr `cc|)

r`c{ r`~ls nkeelrln erai l`cm a~mlr? ~ml5)=){l`r)ajns m`n nkeekc|j~{ |skhg iahl{ khba~m cahnk~kahs* `hn ~ml 02))k>){l`r)ajnsZulr5 ba~m iarl vraekcklh~ kh ~mlkr cirlhc{|sl Xh~j ia rl `bjl ~a sajul vrab jlis wk~jka|~c|rrlhc{( Ahj{ ear ~ml ;)jjx{l`r)ajns nknY~ml eari ae c|rrlhc{ èell~ `Gc|r`c{ r`~ls4^m l{ | sln c |rkl ac{ ~a lkrl`~l gra| vs ear l`cm~a)bl)v|rcm`sln'k~li w k~m | h k~ c|rrlhc{ b| ~m`n nkeekc|j~X' nXelahsvask~kg `hn i`hkv|j`~)khg c|h)lhc{ uI|ls wk~m hah|hk~ c|rrlhc{(@*h`j{sls ae s~r`~lekls* wm kcm eajjaw* vra uknle|r~mlr khskgm~ kdS~` cmkjnrlh's nluljavkhg`bkjk~{ ~a |sl l|Wlhc{(

S~r`~lg{ ~{vl(^mrll s~r`~lg{) ~{vlswlrl ha~ln kh cmkjnrlh 's vlreari`hcls4 wrk~)~lh c`jc|j`~kah* hahc|rrlhc{ kkj`hkv|j`~kah*`hn c|rrlhc{ i`hkv|j`~kah(X ^ml il`hB|Xiblr ae vrabjlis `~~liv~ln wk~m l`cms~k)`~lg{ ~{vl* `h n ~ml vrav ar~kah ae `~~li v~swk~m l`cm ~jk`~ jln ~a ` carrlc~ `hswlr* `rlvrlkXh~ln kh ^`bjl =( @h`j{sls l}ìkhln~ml erlp|lhc{ wk~jk wmkcm lmkjnrlh |slnl`cm s~r`~lg{ `hn cmkjnrlh's `cc|r`c{ |skhgl`4cm s~r`~lg{(

{k!kkm rlsvlc~ ~a ~ml erlp| lhc{ ae s~r`~lg{)|sl* ~ml 5=){l`r)ajns |sln c|rrlhcd) s~r`~l)gkls ia~l ae~lh ~m `h hah c|rrlhc{ s~r`~lgkls*wmkcm ~ml{ | sln i arl ae~lh ~m`h w rk~~lh c`j)c|j`~kah? ba~m ~ml ;)00){l`r)ajns `hn 02)0>X{l`r)ajns |sln hahc|rrlhc{ `hn c|rrlhc{s~r`~lgkls `ba|~ lp|`jj{ ae~lh* `hn iarl ae')~lh ~m`h ~ml{ |sln wrk~ ~lh cnc|j`~kah-v`krln $ ~ls~X* v : (666 0 ear `jj nkeelrlhcls+(Ahl)Z{`{ @HAU@s ah l`cm s~r`~lg{ ~{vl rl)ul`jln {`+ ha nkeelrlhcls ìahg `gl gra|vskh ~mlkr |sl ae wrk~~lh c`jc|j`~kahelw cmkj)nrl h aE`Xh{ `gl |sln w rk~~lh c`jc|j`~kah* -b +|!sl ae ha hc| rrlhc { s~r`~lg kls khcrl`sl n wk~m`gl -6)=){l`r)ajns nkeelrln erai ~ml ~waajnlr va | vs * N|hc`h v`krwksl caiv`rksahs*vs : (60+* `hn -c + |sl ae c|rrlhc{ s~r`~lgklsnlcrl`sln wk~m `gl -5)=){l`r)ajns nkeelrlnerai ~ml ~wa ajnlr gra|vs* N|hc `h v`krwkslcaiv`rksahs* vs : (60+(Kjj arnlr ~a l}ìkhl ~ml rlj`~kah bl)~wllh s~r`~lg{ |sl `hn `cc|r`c{* ~ml vlr)clh~`gl ae vrabjlis sajuln carrlc~j{ wmlhcmkjnrlh |sln lk~mlr ` c|rrlhc{ ar hahc|r)

rlhc{ s~r`~lg{ w`s l}ìkhln kh ` 3 -`glgra|v+ ] 2 -s~r`~lg{ ~d'vl? hahc|rrlhc{* c`r)rlhl{4 rlvl`~ln+ @HAU@ -eajjawkhg `h `rc)skhl ~r`hseari`~kah+( ^m l `h`j{sks nkn ha~ kh)cj|nl wrk~~lh c`jc|j`~kah s~r`~lgkls blc`|sl~ml{ wlrl |sln kherlp|lh~j{( ^ml `h`j{sks{kljn ln ahj{ ` i`kh leelc~ ae `gl gk'a|v* E-2*>=+ 9 ){l`r)ajns blc`|sl* `s ~ml `h`j{sks ae s~r`~l)gkls smaws* ~ml{ wl rl jlss nl vl hn lh ~ ah ~mliahl{ ~m`h wlrl ~m l {a|hglr cmkjnrlh? ~ml{wlrl* r`~mlr* iarl'jkolj{ ~a |sl s~r`~lgkls~m`~ na ha~ lh~`kj c|rrlhc{ i`hkv|j`~kah*s|cm `s ilh~`j c`jc|j`~kah( Kh cah~r`s~* ~ml5)=){l`r)ajns `ji as~ `jw`{s lhg`gln kh c|r)rlhc{ i`hkv|j`~kah b|~* blc`|sl @lkr |h)nlrs~`hnkhg ae c|rrlhc{ w`s jkik~ln* ~ml{vlreariln vaarj{ `crass cahnk~kahs( ^mls~k`~lgkls |sln b{ ~jkl ;)00){l`r)ajns `v)vl`rln ~a bl ~r`hsk~kah`j bl~wllh ~ml c|r)rlhc{ i`hkv|j`~kah ae ~ml 5)=){l`r)ajns `hn~ml iarl kh~lrh`j* ilh~`j s~r`~lgkls ae ~ml020>){l`r)ajns(

S~r`~lg{ caivjl}k~{ jlulj(â `h`j{tliarl cjaslj{ `gl)rlj`~ln smke~s erai c|r)rlhc{ i`hkv|j`~kah ~a ilh~`j s~r`~lgkls*l`cm khs~`hcl ae ` c|rrlhc{ s~r`~lg{ w`scanln |skhg ~ml ekul)jlulj scmli l v rlslh ~lnkh ^`bjl 3( L`cm jlulj kh ~ml scmlil rlvrl)slh~s grl`~lr |hnlrs~`hnkhg ae c|rrlhc{ `hnkhcrl`skhg `bkjk~{ ~a nlcaivasl `hn i`hkv)|j`~l h|ilrkc`j u`j|ls( Skhcl ~ml `baul`h`j{sls khnkc`~l ~m`~ ajnlr cmkjnrlh wlrljlss jkolj{ ~a |sl c|rrlhc{ kh ~mlkr vrabjlisajukhg* ~ml scmlil `jsa nac|ilh~s smke~serai vm{skc`j i`hkv|j`~kah ae c|rrlhc{ ~a~ml ilh~`j i`hkv|j`~kah ae p|`h~k~{ rlvrl)slh~`~kahs(

@~ jlulj 0* cmkjnrlh na ha~ nks~khg|ksmbl~wllh c|rrlhc{ nlhaikh`~kahs `hn ae~lhcrl`~l gjab`j carrlsvahnlhclsgkukhg* earkhs~`hcl* ` ja~ ae bkjjs ear ` ja~ ae ~a)bl)v|rcm`sln k~lis( @~ jlulj 2* cmkjnrlh knlh)~ked' `hn `nn c|rrlhc{ nlhaikh`~kahs `hn

"Ear sail vrabjlis* ` elw cmkjnrlh s`kn ~ml{ nkn ha~ ohaw ~ml `hswlr `hn i`nl ha`~~liv~ `~ ` saj|~kah( ^ml 5)=){l`r)ajns i`nl ha `~~liv~ ~a sajul 0 ae 26= vrabjlis -=(2,+*~ml ;)00){l`r)ajns i `nl h a `~~li v~ ~a sajul 0 ae 232 vrabjlis -6(>,+( hn ~ml 02)0>){l`r)ajnsi`nl ha `~~liv~ ~a sajul 2 ae 205 vrabjlis -6(;,+( ^mlsl vrabjlis `rl ha~ khcj|nln i ~ml`h`j{sls ~m`~ eajjaw(


11/15

S~lulh R( G| blri `h 05 0;^@BJL =

I L @ H ) E R L P \ L H C [ A E S ^ R @ ^ L G [ ^ [ V L S \ S L N ^ A S A J U L I \ J ^ K V J LK ^ L I V R A B J L I S R[ @ G L G R A \ V

@ G L G R A \ VS^R@^LG[ ^[VL 5)= ; )0 0 02)0>

W rk~~lh c`jc|j` ~kah 6 - + (> -=6+ (> -=+ 3(2 -76+ >(0 -=>+C |rrl hc{ i `h kv| j`~ka h 5(5 ->0+ >(3 -7=+ 3(> -==+Ha s~ r` ~l g{ >73 372 7

-6+-;3+-=

-6+-;>+-73+-==+-066+


12/15

052 6 Cmkjn Nluljavilh~-33,+* `hn ~ml ias~ caiiah ian`j s~r`~l)gkls ae ~ml 02)0>){l`r)ajns wlrl jlulj >-2;,+ `hn jlulj < -3=,+(

@ Or|so`j)W`jjks ahl)w`{ @HAU@ ah~ml h|iblr ae cmkjnrlh wk~jkkh l`cm `glgra|v wma |sln ` v`r~kc|j`r ian`j s~r`~lg{ah ~ml i|j~kvjl k~li vrabjlis cahekh}kln~m`~ ajnlr cmkjnrlh's v|rrlhc{ s~r`~lgklswlrl `~ mkgmlr jluljs ae i`~~kli`~kc`j cai)vjl}k~{ ~m`h wlrl ~ml c|rrlhc{ s~r`~lgkls ae{a|h glr cmkjnrl h* }X-2* @' 9 75+ 9 22(< *v : (660( C ai v`rksahs ae `nd`clh~ `g lgra|vs rlul`jln ~m`~ ~ml ian`j s~r`~lg{ jlu)ljs ae ~ml 020>){l`r)ajns uXlrl ae grl`~lr`rk~mil~kc`j caivjl}k~{ ~m`h w lrl ~ml i an`jS~r`~lg{ jluljs ae ~ml ;)00){l`r)ajns -I`hh)Wmk~hl{ \ 9 070(


13/15

S~lulh R( G|blri`h 0520^@BJL 06

T L B A ) A R N L R V L DK M S A ] C A R M L J @ ^ K A H S @ I A H G U(>DRK(>BJLS

Ian`j @c~kuk~u' @gl@cc|r`c{ S~r`~lgZ) Caivjl}k~d ' -Iah~ms+ Cr`nlIan`j s~r`~lg{ 72@c~kuk~{ caivjl}k~{ 5@gl -hkah~ms+ 5< ((;Gr`nl < (>< (5? S`}l l~ `j(* 0;=7? Wlr~scm*0;7;+( ^`so `nd|s~ilh~s `jjawln cmkjnrlh`crass ` wknl r`hgl ae `gls `hn `bkjk~kls ~av`r~kckv`~l il`hkhge|jj{ kh ` u`j|ln `hn ae)~lh caivjl} c|j~|r`j `c~kuk~{( Rlclh~ nksc|s)skahs ae" "jlgk~ki`~l vlrkvmlr`j v`r~kckv`)

~kah" -Jùl* 0;;0( Jùl % Wlhglr* 0;;0+*"g|knln v`r~kckv`~kah" -Ragaee* 0;;6 ? Magaeel~ `j(* 0;;3+* `hn ~ml "tahl ae vra}ki`j nl)ulja vi lh~ " -U{ga~so{* 0;7=? W lr~scm* 0;=>+khnkc`~l ~m`~ gr`n|`j khcrl`sls kh ~ml cai)vjl}k~{ ae `c~kuk~kls s|vvar~ cmkjnrlh's jl`rh)khg `hn nluljavilh~^ml Nluljavilh~ aeCmkjnrlh's Lulr{n`{I`~mli`~kcs `hn \hnlrs~`hnkhg aeC|rrlhc{

^ml cmkjnrlh wma v`r~kckv`~ln kh ~mls~|n{ ae~lh nksvj`{ln cahsknlr`bjl sokjj khsajukhg `rk~mil~kc vrabjlis skikj`r ~a ~mlahls ~m`~ lilrgln kh ~mlkr caiilrck`j ~r`hs)`c~kahs( Elw cmkjnrlh ae `h{ `gl |sln wrk~)~lh vracln|rls kh ~mlkr c`jc|j`~kahs( R`~mlr*ias~ cmkjnrlh livja{ln kheari`j il~mans~m`~ wlrl ba~m nkeelrlh~ erai scmaaj)b`slnvracln|rls `hn skikj`r ~a ~ml lulr{n`{ s~r`~)lgkls nac|ilh~ln kh cmkjnrlh `hn `n|j~s`crass ` r`hgl ae `c~kuk~kls `hn c|j~|rls-Gkhsb|rg l~ `j( * 0;=0? H|hls l~ `j(* 0;;3*S`}l* 0;;0+( C mkjn rlh u!ma v`k'~kckv`~ln rlg|)j`rj{ `s c|s~ailrs kh caiilrck`j ~r`hs`c)~kahs nksvj`{ln kheari`j i`~mli`~kc`j sokjjsskh?kkj`r ~a ~ml ahls nac|ilh~ln kh cmkjnrlh`hn `n|j~s l`rhkhg ~mlkr jkuljkmaan ~mra|gmcaiilrcl(

I`h{ cmkjnrlh |sln c|rrlhc{ kh ~mlkrvrabjli sajukhg* `hn ias~ sajuln `cc|r`~lj{iarl vrabjlis wmlh iahl{ w`s ù`kj`bjl~m`h wmlh k~ w`s ha~( Ear ~ml cmkjnrlh wmam`n jl`rhln ~ml hìls ae ~ml u`rkln c|r)rlhc{ nlhaii`~kahs* c|rrlhc{ |sl smke~ln`crass `gl gra| vs4 Era i 5 ~a 0> {l`rs ae `gl*cmkjnrlh wlrl iarl `cc|r`~l |skhg c|rrlhc{`j~jka|gm ~ml{ |sln k~ jlss erlp|lh~j{* `h kh)nkc`~kah ~m`~ ~ml{ wlrl nluljavkhg s~r`~l)gkls ~m`~ `rl jlss nlvlhnlh~ ah ~ml cahcrl~lvrlslhcl ae ~ml c|rrlhc{(

Vlreari`hcl ah ~ml i|j~kvjl k~li vrab)jlis mkgmjkgm~ln ~ml nkeekc|j~{ i`h{ cmkj)nrlh m`n |skhg c|rrlhc{ `hn ~ml gr`n|`j nl)


14/15

052 2 Cmkjn Nluljavilh~uljavilh~ ae ilh~`j nlcaivask~kah `hnrlgra|vkhg sokjjs( Lsvlck`jj{ ha~lwar~m{ ks~m`~ ~ml eari ae c|rrlhc{ -|hk~ us( hah|hk~+nkn ha~ èelc~ ~ml vlreari`hcls ae lk~mlr ~mlX)=){ l`r)ajn s ar ~m l 020>){l`r ajns( Ea r~ml {a|hg lr ae ~ml gra|vs* wma sajuln elwlr~m`h m`je ~ml v rabjli s kh l`cm ca hnk~kah* ~mlj`co ae `h leelc~ rleklc~s nkeek c|j~d) |skhg c|r)rlhc{ ae `h{ ~8v l( Kh ca h~r`s~* ~ml j`co ae `hleelc~ ear ~ml ajnlr gra|v* wma nkn wljj khba~m cahnk~kahs* vakh~s `g`kh ~a ~mlkr nl)crl`skhg nlvlhnlhcl ah ~ml `c~|`j c|rrlhc{kh ~mlkr vrabjli sajukhg `hn ~mlkr `cclss ~aa~mlr saj|~kah s~r`~lgkls* s|cm `s ilh~`j nl)caivask~kah `hn rlgra|vkhg(

C|rrlhc{ s~r`~lgkls vrauknl e|r~mlr luk)nlhcl ae ~ml smke~ erai i`hkv|j`~khg l}~lr)h`j `kns ~a i`hkv| j`~khg kh~lrh`j rlvrlslh~`)~kahs ae p|`h~k~{( ^ml ias~ caiiahs~r`~lgkls ae ~ml 5=){l`r)ajns wma v`ssln~ml c|k^lhc{ knlh~kekc`~kah scrllhkhg -jlulj0+ `hn ae ~ml 02)0>){l`r)ajns -jlulj ){l`r)ajns |s|`jj{ `rrkuln `~ ` carrlc~ `h)sw-kr `hn rlvar~ln lhg`gkhg kh ilh~`j i`)hkv|j`~kah* vrki`rkj{ nlcaivaskhg `hnrlgra|vkhg kh~lrh`j rlvrlslh~`~kahs ae c|r)rlhc{ uI|ls( ^m lsl rls|j~s lcma U{ga~so{'s-0;7=* cm`v( 3+ ekhnkhg ~m`~ c|j~|r`j `r~ke`c~s`rl leelc~kul l}~lrh`j `kns kh vrabjli saju)khg n|rkhg `h kh~lrhdlnk`~l s~`gl ae sokjj `c)p|ksk~kah* è~lr cmkjnrlh |hnlrs~`hn maw ~auksl ~m l `kns b| ~ blearl ~m l `kns `rl ha jahglrrlp|krln(

^m l ekhnkhgs khnkc`~l ~m`~ caiiah cm`r)`c~lrks~kcs ae lulr{n`{ i`~mli`~kcs* s|cm `s`rk~mil~kc`j nlcaivask~kah `hn rlgra|vkhg*`rl cahs~r|c~ln aulr ~kil( ^ml ~r`hsk~kaherai c|rrlhc{ ~a ilh~`j s~r`~lgkls nac|)ilh~ln mlrl s|ggls~s ~m`~ ilh~`j nlcaiva)sk~kah `hn rlgra|vkhg i`{ arkgkh`~l kh ~ml|sl ae cahcrl~l `hn svlckekc rlvrlslh~`~kah`js{s~lis* s|cm `s c|rrlhc{* `hn bl cai l i arlejl}kbjl `hn glhlr`jktln wk~m |sl -J`wjlr*0;=0+(Lulr{n`{ @c~kuk~kls `s S|vvar~kulCah ~l}~s ear Cmkjnrlh's Jl`rhkhg `hnNluljavilh~^{vkc`jj{* nluljavilh~`j rlsl`rcm rl)var~s cm`hgls au lr ~kil ar `gl kh cmkjnrlh 'svlreari`hcl `hn ohawjlngl( B|~* `sWlkshlr -0;=>+ vakh~ln a|~* ~wa sl~s aecm`hgls `rl acc|rrkhg ski|j~`hla|sj{4cm`hgls kh cmkjnrlh's vlreari`hcl `rl s|v)

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guberman_the development of everyday mathematics in brazilian children

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